From Mirrors to Lenses

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From Mirrors to Lenses
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c
f
real image
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Real Images
Rather than a virtual image (which is formed by
virtual rays), a real image is formed by real
rays! It can only be produced by a concave
mirror, and only if the object is further than
the focal point. Since the image is formed by
actual rays of light in front of the mirror, it
can be projected onto a screen. You need to see
it to believe it..
4
Concave Mirror Object further than c
Color Code
P-ray
F-ray
C-ray
c
f
The image is real, inverted, and reduced.
5
Concave Mirror Object at c
Color Code
P-ray
F-ray
C-ray
f
c
The image is real, inverted, and the same size as
the object.
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Concave Mirror Object between c and f
Color Code
P-ray
F-ray
C-ray
f
c
The image is real, inverted, and enlarged.
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Concave Mirror Object at focal point
Color Code
P-ray
F-ray
C-ray
c
f
These will never intersect
NO IMAGE IS FORMED!!!
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Concave Mirror Object closer than f
Color Code
P-ray
F-ray
C-ray
f
c
The image is virtual, upright, and
enlarged. This is why concave mirrors with large
focal lengths are used as makeup mirrors!
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Concave Mirrors Summary
Object Location Image Orientation Image Size Image Type
Beyond c Inverted Reduced Real
At c Inverted Same as object Real
Between c and f Inverted Enlarged Real
At f No image No image No image
Closer than f Upright Enlarged Virtual
If the object is further than f, the image will
be inverted and real. If the object is closer
than f, the image will be upright and virtual.
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Convex Mirror Object anywhere
Color Code
P-ray
F-ray
C-ray
c
f
The image is virtual, upright, and reduced.
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Convex Mirrors Summary
Object Location Image Orientation Image Size Image Type
Anywhere Upright Reduced Virtual
This is why convex mirrors are used for seeing
large areas at once!
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Real vs Virtual Images
Real images are formed by actual light rays (not
virtual rays). They are able to be seen directly
with the human eye, and can also be projected
onto a screen! Virtual images are formed by
virtual rays. A virtual image is the appearance
of light originating from a certain location,
although the light never actually did (it was
redirected by a mirror or lens to look like it
did!) When a virtual image is formed, it can be
seen by the human eye. However, it cannot be
projected onto a screen!
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What is a lens?
A lens is a piece of transparent material that is
shaped such that the outside is curved on at
least one side. There are many types of lenses,
and the two that we will concentrate on in this
course are convex lenses and concave lenses.
Convex lens
Concave lens
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The types of lenses that we will be learning
about are circular in curvature on both sides.
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Convex Lens
focal point
c
Incoming rays that are parallel to the principal
axis will all pass through the focal point! This
type of lens is sometimes called a converging
lens.
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Focal point depends on n of lens and medium that
it is in! Lenses actually have a focal point on
both sides.
f
f
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We will be Working with Thin Lenses
This means that you dont need to worry about
light refracting as it enters and as it leaves
the lens. You only need to know how to use
concepts to draw principal rays. It also means
that a light ray passing through the center of
the lens (at any angle) will pass directly
through the lens, undeflected!
The thin lens assumption allows us to draw this
ray. With thick lenses, a more complex approach
is required.
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Principal Rays for Lenses!
The principal rays used to locate the image
formed by a lens are very similar to the ones
used with curved mirrors! The concepts are also
very similar. Make sure to pay attention to the
concepts, as well as the specific rules for each
ray.
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P-Ray (Parallel Ray)
Emitted by the object, traveling parallel to the
principal axis. It is then refracted through the
focal point!
f
f
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F-Ray (Focal Ray)
Emitted by the object, traveling through the
focal point. It is then refracted parallel to
the principal axis!
f
f
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C-Ray (Center Ray)
Emitted by the object, traveling toward the
center of the lens. It passes through
undeflected!
f
f
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Concave Lens
antifocal point
Incoming rays that are parallel to the principal
axis will diverge directly away from the
antifocal point! This type of mirror is
sometimes called a diverging lens.
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P-Ray Concave Version
Emitted by the object, traveling parallel to the
principal axis. It is then refracted directly
away from the antifocal point!
f
f
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F-Ray Concave Version
Emitted by the object, toward the antifocal point
on the other side of the lens. It is then
refracted parallel to the principal axis!
f
f
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C-Ray Concave Version
Emitted by the object, traveling toward the
center of the lens. It passes through
undeflected!
f
f
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Concave Lens Object at any location
Color Code
P-ray
C-ray
c
f
f
c
The image is virtual, upright, and reduced.
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Virtual Images in Mirrors vs Lenses
For mirrors, a virtual image will always be on
opposite side as the object. Convex mirrors
always produce virtual images.
For lenses, a virtual image will always be on the
same side as the object. Concave lenses always
produce virtual images.
c
f
c
f
f
c
Rays appear to diverge from behind the mirror.
Rays appear to diverge from in front of the lens.
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Concave Lenses Summary
Object Location Image Orientation Image Size Image Type
Anywhere Upright Reduced Virtual
This is the same as for a convex mirror!
Converging lenses and converging mirrors have the
same image properties. Diverging lenses and
diverging mirrors have the same image properties.
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Convex Lens Object further than c
Color Code
P-ray
F-ray
C-ray
c
f
f
c
The image is real, inverted, and reduced.
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Real Images in Mirrors vs Lenses
For mirrors, a real image can only be produced by
a concave mirror, and the image is on the same
side as the object.
For lenses, a real image can only be produced by
a convex lens, and the image is on the opposite
side as the object.
Rays converge in front of the mirror.
Rays converge behind the lens.
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Convex Lens Object at c
Color Code
P-ray
F-ray
C-ray
c
f
f
c
The image is real, inverted, and the same size.
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Convex Lens Object between c and f
Color Code
P-ray
F-ray
C-ray
c
f
f
c
The image is real, inverted, and enlarged.
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Convex Lens Object at f
Color Code
P-ray
F-ray
C-ray
c
f
f
c
No image is formed!
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Convex Lens Object closer than f
Color Code
P-ray
F-ray
C-ray
c
f
f
c
The image is virtual, inverted, and enlarged.
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You now have all of the tools necessary to locate
an image formed by any curved mirror or
lens. Geometric optics is covered on the AP
test, so you should go over this again in your
AP review book in the next few weeks. Go forth
and make me a proud physics teacher ) (and get
college credit for this course)
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Convex Lenses Summary
Object Location Image Orientation Image Size Image Type
Beyond c Inverted Reduced Real
At c Inverted Same as object Real
Between c and f Inverted Enlarged Real
At f No image No image No image
Closer than f Upright Enlarged Virtual
This is the same as for a concave mirror! This
is why convex lenses held close to an object make
good magnifying glasses!
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Concave Lenses Summary
Object Location Image Orientation Image Size Image Type
Anywhere Upright Reduced Virtual
This is the same as for a convex mirror!
Converging lenses and converging mirrors have the
same image properties. Diverging lenses and
diverging mirrors have the same image properties.
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Enlightening Concept!
A large lens is used to focus an image of an
object onto a screen. If the left half of the
lens is covered with a dark card, which of the
following occurs?   (A) The left half of the
image disappears. (B) The right half of the image
disappears. (C) The image becomes blurred. (D)
The image becomes dimmer. (E) No image is formed.
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Although principal rays help guide us to locate
the image, we cannot forget the important fact
that each point on the object emits rays in all
directions. The lens is completely filled with
rays from every point of the object!
(The image is also formed by infinite rays from
the middle of the object, the bottom of the
object, etc.)
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So, if we cover half of the lens...
The entire image would still exist! However,
less light would be forming the image. Therefore
the image would be dimmer.
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Which three of the glass lenses above, when
placed in air, will cause parallel rays of light
to converge? (A) I, II, and III (B) I, III,
and V (C) l, IV, and V (D) II, III, and IV (E)
II, IV, and V
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I, III, and V are more convex than concave they
will cause light rays to converge. II and IV are
more concave than convex they will cause light
rays to diverge.
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Geometric Optics Equation 1
Applies to both mirrors and lenses.
di is the distance from the image to the mirror
or lens do is the distance from the object to
the mirror or lens f is the focal length of the
mirror or lens
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Focal length can be positive or negative!
Mirrors and lenses that have a focal point will
have a positive focal length. Mirrors and lenses
that have an antifocal point will have a negative
focal length. Converging lenses and mirrors
(concave mirrors and convex lenses) have a
positive focal length. Diverging lenses and
mirrors (convex mirrors and concave lenses) have
a negative focal length.
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A Point of Possible Confusion

• Real images have a positive di
• Virtual images have a negative di
• If you end up with a negative di when you do the
  calculations, it means that a virtual image is
  produced!
• This applies to both mirrors and lenses, and you
  must be consistent!

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Whiteboard Problem Solving I
A postage stamp is placed 30 centimeters to the
left of a converging lens of focal length 60
centimeters. Where is the image of the stamp
located? (A) 60 cm to the left of the lens
(B) 20 cm to the left of the lens (C) 20 cm
to the right of the lens (D) 30 cm to the right
of the lens (E) 60 cm to the right of the lens
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Whiteboard Problem Solving II

• A concave mirror with a radius of curvature of
  1.0 m is used to collect light from a distant
  star. The distance between the mirror and the
  image of the star is nearly
• 0.25 m (B) 0.50 m (C) 0.75 m
• (D) 1.0 m (E) 2.0 m

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Solution!
A star is so far away that we can comfortably use
the approximation do 8!
This gives
Since 1/8 0, this results in di f
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Geometric Optics Equation 2
hi is the height of the image ho is the height
of the object A negative image height means that
the image is inverted. Memorize both of these
equations (dont forget the negative sign!)
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Attack of the Whiteboard
15 cm
5 cm
f
f
10 cm
10 cm
Where will the image be located and what will it
look like?
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do 15 cm f -10 cm
di -6 cm
(Virtual image 6 cm from lens)
hi 2 cm
ho 5 cm
(Inverted and reduced image)
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Deep Whiteboard Thoughts!
do
An object of height h0 is located at a distance
do from a plane mirror.
ho
Using the mathematical models
and ,
determine the location and height of the image
formed by the plane mirror!
Hint What is the radius of curvature of a plane
mirror?
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do
fplane mirror 8
ho
0!
di -do
Since di -do ? -di / do 1 Therefore hi
/ ho 1 hi ho The image is the same height as
the object!
This means that the mirror will produce a virtual
image (negative image distance) that is
equidistant from the mirror.